Question

Which of the following has one solution? Select all that apply.A) 10x+5=3(5x+7)B) 5x-10=x+20C) 2(6+x)=14+2xD) 2(4+x)=8+2x

Answer 1

Finding the solution of each equation, we have:

a)

`\begin{gathered} 10x+5=3(5x+7) \\ 10x+5=15x+21 \\ 5x=-16 \\ x=-3.2 \end{gathered}`

This system has one solution.

b)

`\begin{gathered} 5x-10=x+20 \\ 4x=30 \\ x=7.5 \end{gathered}`

This system has one solution.

c)

`\begin{gathered} 2(6+x)=14+2x \\ 12+2x=14+2x \\ 12=14 \end{gathered}`

This system has no solutions.

d)

`\begin{gathered} 2(4+x)=8+2x \\ 8+2x=8+2x_{} \\ 8=8 \end{gathered}`

This system has infinitely many solutions.

So the correct options are A and B.